Aggressive : If a monster comes within range of the pet, the pet moves to attack the monster.

Defensive : The pet responds if attacked but otherwise won't act.

Passive : The pet just sits there and does not attack. This is useful if you want to stop a pet from attacking to play around with hate lists or for other reasons. It comes in handy.

Pet Control
You need to manage the hate of the monster between you and your pet. The monster attacking your pet is about to kill it then you need to either heal your pet or get the monster to attack you instead. You can transfer the monster over to you by casting spells on the monster that really make it angry. You will have to figure out which spells do that.

If the monster is too focused on you, you need to stop attacking it and use whatever pet abilities your pet has to make the monster angry enough to fight it instead. Learning how to properly manage monster hate can take some time. The goal is to keep both you and your pet alive until the end of combat.

If you're in a party and your pet is attracting too much attention, have it stop attacking until the monster focuses on someone else in the party. Then wait a bit longer and have your pet rejoin the fight again. That way your pet can continue to attack and live while the monster is attacking someone else.

When you give your pet commands it will cancel any spells they are currently casting.

Rookie Mistakes
If your pet is in Aggressive mode inside of a dungeon it will typically go crazy and wake up lots of monsters. Change it to Passive or Defensive mode.

When traveling, make sure your pet is not in Aggressive mode. Otherwise, your pet will really slow you down by attacking everything you pass. You should either change it to Passive mode or unsummon the pet if you don't think you will need it.

At the start of a battle make sure your pet is attacking. If it is standing around, it's not helping. You can use hot keys to make your pet attack faster. To make the pet attack, press Control and 1 buttons at the same time.

Pet Fun
Go into a newbie region and use your pet to destroy some monsters. It is funny to have your pet do all the work as you watch!
Kill someone with your pet in player vs. player combat!

Use emotes on your pet! /hug pet =]
Use powerful pets to scare newbies. They will think it's a monster if they are not familiar with the pets that players can use.

Other Information
Pets, summons and guardians are not susceptible to charm.
Pets and summons will use their combat abilities as often as possible.

If you tell your pet to attack a creature, it won't be distracted unless taunted.
The pet action bar is greyed out while the pet is confused or fleeing.

Pets of other party members display in the party UI. You can see pet health and harmful effects on the pet. You can turn this functionality on and off in the Interface Options menu.

Common Pet Questions

Can I give items to my pet?

No.

Can I name my pet?

Hunters can name their pets. Warlocks cannot.

Do pets take up extra experience?

No.

What classes get pets?

Warlocks and Hunters can get permanent pets. Priests can control humanoid monsters as a pet for a limited amount of time. There are other ways to get pets. For example, Engineers can construct pets. There are items that players can find that create a pet for a limited amount of time. Players can also buy non-combative pets that are purely for show.